Is my logic correct below to prove the Pythagoras Theorem? Thanks.
Area Rectangle R
\begin{align*}
R &= WL\\
&=(2a+b)(2b+a)\\
&=4ab+2a^2+2b^2+ab\\
&=5ab+2a^2+2b^2
\end{align*}
Total Area Yellow Triangles T
\begin{align*}
T &= 10(\frac{ab}{2})\\
&=5ab
\end{align*}
Calculate Area $c^2$
\begin{align*}
c^2 &= R-T-a^2-b^2 \\
&=5ab+2a^2+2b^2-5ab-a^2-b^2\\
&=a^2+b^2
\end{align*}
∎
Proof by rearrangement
Best Answer
Yes. This is correct provided you have shown that all yellow triangles are congruent.